Abstract. In the present paper we introduce the lower autocentral seriesof autocommutator subgroups of a given group. Following our previouswork on the subject in 2009, it is shown that every nite abelian groupis isomorphic with n th -term of the lower autocentral series of some niteabelian group. 1. IntroductionLet A = Aut( G ) denote the group of automorphisms of a given group G . Forany element g 2 G and 2 A the element [ g; ] = g 1 g is an autocommutator of g and : We de ne the autocommutator of higher weight inductively asfollows:[ g; 1 ; 2 ;:::; i ] = [[ g; 1 ; 2 ;:::; i 1 ] ; i ]for all 1 ; 2 ;:::; i 2 A: So the autocommutator subgroup of weight i + 1 is de ned in the followingway: K i ( G ) = [ G;A;:::;A | {z } i -times ] = ⟨ [ g; 1 ; 2 ;:::; i ] j g 2 G; 1 ; 2 ;:::; i 2 A⟩: Clearly K i ( G ) is a characteristic subgroup of G for all i  1. Therefore, oneobtains a descending chain of autocommutator subgroups of G as follows: G  K 1 ( G )  K 2 ( G )   K i ( G )  ; which we may call it the